I have a really weird and vague idea in my head that I don't think I'll write because I don't know how but let me try to put it into words here anyway
But like. What if the exchange program is the first time the brothers are all home together in a long time? (I'm sure there are canon details to debunk this immediately so if so consider this an AU of sorts)
Mammon is away so often, running from debt collectors and hiding from the consequences of his actions. He spends random weeks away from school only to return with either a suspiciously expensive-looking accessory or a new injury to the jaw and manages to scrape by his classes with the little material he is present to learn.
Satan does NOT want to be home so after school, he spends his time in bookstores and then spends nights at 24-hour libraries. On weekends and vacations he travels around the Devildom or crashes with one of his connections. He probably has a full-on abode just somewhere for him to be away.
Asmodeus has plenty of company and, rather than taking people home, allows them to take him home. He seduces his pact holders when in desperate need of a place to stay but can generally afford to keep himself in a nice hotel for a while (or get the connections to have somebody else buy them for him)
I'm reading a fic where Beel also has some military status (if i find it ill link it!) so he's off doing that, training recruits and meeting with officials. Or he disappears to try various sports that require different environments than the city has to offer. Sometimes he meets up with Belphie and hangs out with him if he has time, but nobody else ever knows when or where this happens.
Lucifer and Leviathan both stay home but almost never see each other. The little D's do the chores while Lucifer works and bring food to Levi, who still only leaves his room for school and Navy events. Even for special merchandise drops, he manages to get others to get the merch for him instead of getting it himself. Lucofer is frequently at the palace for his work and spends long stretches of time never going home once. Occasionally they run into each other in the halls or the kitchen and it is SO awkward.
The only person I'm not 100% on is Belphie. Maybe he still stays at home but he sleeps the whole time and then sneaks out at night or when he has plans with Beel. Sometimes he runs away for long stretches of time and doesn't go to school, magically appearing on test days and managing to ace them before disappearing again. He sort of floats around.
Then the exchange program is set into motion, and the brothers are told they have to stay in the HoL in order to be available to the human.
This is part of the reason they are so chaotic around MC - they've spent too much time apart and don't know how to mesh into a family structure anymore. They had sparse time to adjust to the co-inhabitation and now there's a human they have to pretend to care about? They are having a Hard Time adjusting.
But Mammon finds himself trying to get himself into less trouble - he really doesn't want to kure anybody dangerous back to his brothers, even if they could handle whoever it is.
Leviathan wanders the house more, partially because the walls are thick but not block-out-five-other-demons thick, and finds himself just existing near other people more.
Satan realizes how nice it is to have books around him that he owns, and a place where he can keep possessions that are his (that he wouldn't have to carry from place to place of he was crashing) and also not be entirely alone. A quiet house at 2 am is more peaceful than scary when you know there are people sleeping in it.
Asmodeus can't bring people home anymore, but he finds his brothers to sometimes be decent conversation partners. He also forgot how much fun it was to do somebody's hair and/or makeup and gossip or be able to give advice. He feels a little more like a person.
Beel loves being with his brothers again, and even though he misses Belphie, he hopes all seven of them will be able to be together for a little while before they all split off again at the end of the program.
Belphegor is already seething with rage, and doing a horrible job at dealing with his grief and betrayal. But sometimes, it calms him down when he lies on the floor with one ear pressed against the wood, and he can hear everybody talking at dinner. He tricks himself into thinking he doesn't wish he were with them.
Lucifer is glad to have all of his brothers under one roof again, and when he passes someone in the hall there's a secret smile on his face once he's behind them and they can't see. But sometimes, when he's tired and trudging through the halls at night, he checks on Belphegor in his room and startles when he isn't there. Lucifer thinks, for a moment, that he ran away again, before remembering the much more brutal truth.
And this is why they cling to you, in part. Not only did you help them fix their underlying issues, but you brought them back together in the first place.
